Weakly nonlinear theory predicts supercritical behaviour in the high elasticity (\(Wi/Re\) ) regime, i.e., along the lower boundary of the linearly unstable region.
To probe this, a fifth branch was initiated at fixed \(Wi = 60\) , starting upwards in \(Re\)  as indicated by the weakly nonlinear analysis [1]} from a marginally stable point in this region (indicated by orange on Figure REF ). The resulting branch of solutions is shown in Figure REF . Given the supercriticality, this branch starts off as a stable node, moving up in \(Re\) . Almost immediately after leaving the initial bifurcation point (of linear stability), it reaches a saddle-node bifurcation point, turns around and proceeds to advance towards decreasing \(Re\) , maintaining a relatively low amplitude until reaching a second saddle-node and transitioning to the upper branch. This is an example of how local information provided by weakly nonlinear analysis can be misleading. In fact, the neutral curve gives rise to TWs which reach to lower \(Wi\)  at fixed \(Re\)  and lower \(Re\)  at fixed \(Wi\)  as shown by Figure REF .
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